No, there is no direct ferry from Fethiye to Bodrum. However, there are services departing from Fethiye and arriving at Bodrum via Rhodes. The journey, including transfers, takes approximately 4 h 50 min.

Bodrum, Turkey

Bodrum is a district and a port city in Muğla Province, in the southwestern Aegean Region of Turkey. It is located on the southern coast of Bodrum Peninsula, at a point that checks the entry into the Gulf of Gökova, and is also the center of the eponymous district. The city was called Halicarnassus of Caria in ancient times and was famous for housing the Mausoleum of Mausolus, one of the Seven Wonders of the Ancient World. Bodrum Castle, built by the Knights Hospitaller in the 15th century, overlooks the harbour and the marina. The castle grounds include a Museum of Underwater Archaeology and hosts several cultural festivals throughout the year. The city had a population of 36,317 in 2012.
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Things to do in Bodrum

Bodrum Castle (Turkish: Bodrum Kalesi), located in southwest Turkey in the port city of Bodrum (37°1'54"N 27°25'46"E), was built from 1402 onwards, by the Knights of St John as the Castle of St. Peter or Petronium.

The Mausoleum at Halicarnassus or Tomb of Mausolus (Ancient Greek: Μαυσωλεῖον τῆς Ἁλικαρνασσοῦ; Turkish: Halikarnas Mozolesi) was a tomb built between 353 and 350 BC at Halicarnassus (present Bodrum, Turkey) for Mausolus, a satrap in the Persian Empire, and his sister-wife Artemisia II of Caria. The structure was designed by the Greek architects Satyros and Pythius of Priene.

The Tree of Hippocrates is the plane tree (or platane, in Europe) under which, according to legend, Hippocrates of Kos (considered the father of medicine) taught his pupils the art of medicine. Paul of Tarsus purportedly taught here as well. The Platanus in Kos is an oriental plane (Platanus orientalis), with a crown diameter of about 12 metres, said to be the largest for a plane tree in Europe.

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